If g is a differentiable function such that g(x) < 0 for all real numbers x and if f'(x)=(x2-4)g(x), which of the following is true
nswered Suppose that a function f satisfies the following conditions for all real values of x and y: 1. f(x+y)=f(x).fl) 2. f(x)= 1+xg(x), where lim g(x)=1. ut of 200 question X +0 Then f is differentiable at all real numbers x and f(x)= f(x). Select one: o True O False
Suppose that the function f is defined, for all real numbers, as follows. f(x) = x-2 ifx#2 4 if x=2 Find f(-3), f(2), and f(5). s(-3) = 0 s(2) = 0 r(s) = 1 Suppose that the function g is defined, for all real numbers, as follows. if x -2 8(x)= 1-4 if x=-2 Find g(-5), g(-2), and g(4). $(-5) = 0 DO s(-2) = 1 8(4) = 1
Suppose that f(x) is a continuous function over all real numbers, f'(- 10) = 0, and f''( - 10) = 24 Which of the following is true? (Hint: 2nd derivative test) Which of the following is true? (Hint: 2nd derivative test) O A. f(x) has a relative minimum at x = - 10 W O B. f(x) is decreasing when x = - 10 O C. f(x) is increasing when x = - 10 O D. f(x) has a relative...
Determine if the following piecewise defined function is differentiable at x = 0. x20 f(x) = 4x-2, x2 + 4x-2, x<0 What is the right-hand derivative of the given function? f(0+h)-f(0) lim (Type an integer or a simplified fraction. I h h+0+
Real analysis 7. Assume that f and g are differentiable functions such that f(0) 9(0) and that for all & ER, S' () > '(x). Prove that f(c) > 9() for all > 0.
5. This problem concerns a function , about which the following information is known . fis a differentiable function defined at every real number x. y-f'(x) has its graph given in the middle picture below S. This problem concerns a function f, about which the following information is f is a differentiable function defined at every real number x. y(x) has its graph given in the middle picture below. Construct a first derivative sign chart for f. Clearly identify all...
1. Suppose that a function f, defined for all real numbers, satisfies the property that, for all x and y, f(x + y) = f(x) + f(y). (*) (a) (2 points) Name a function that satisfies property (*). Name another that doesn't. Justify your answers. (b) (3 points) Prove that any function that satisfies property (*) also satisfies f(3x) = 3f(x). (c) (5 points) Prove that any function that satisfies property (*) also satisfies f(x - y) = f(x) –...
1. Suppose that a function f, defined for all real numbers, satisfies the property that, for all x and y, f(x + y) = f(x) + f(y). (*) (a) (2 points) Name a function that satisfies property (*). Name another that doesn't. Justify your answers. (b) (3 points) Prove that any function that satisfies property (*) also satisfies f(3x) = 3f(x). (c) (5 points) Prove that any function that satisfies property (*) also satisfies f(x - y) = f(x) –...
True or False If f is differentiable everywhere and f^′(x)<0 for all x, then lim x→∞ f(x)= −∞
Question 4 (1 point) if f(x) is a one-to-one differentiable function with f(a) f'(a) +0, then f'(0) (-)'(a) = 1. = band True False Question 5 (1 point)